Method for constructing a balanced stair

ABSTRACT

For designing a balanced stair comprising steps with treads ( 1 - 15 ) showing front edges ( 26 ), a line of travel ( 22 ) is determined on the stair and a reference line is determined onto each step in a predetermined position with respect to the front edge ( 26 ) thereof. In contrast to the prior art methods wherein the reference lines, more particularly the front edges ( 26 ) or the risers ( 25 ) of the steps, are divided along the line of travel ( 22 ) on constant mutual distances measured on the line of travel itself, the substantially constant mutual distances (d) between the reference lines is determined according to the invention near the line of travel ( 22 ) along a measuring line ( 27 ) which is determined for each pair of adjoining reference lines so as to form a substantially constant angle (α) with at least one of the adjoining reference lines thereof. In this way, a stair which is easier to walk on and which automatically shows a more regular nosing line at the outer string ( 21 ) is obtained

[0001] The present invention relates to a method for constructing abalanced stair comprising steps with treads showing front edges, whichmethod comprises the step of designing the stair and the step ofmaterially constructing the stair so designed, the designing stepcomprising the step of determining a line of travel on the stair, thestep of determining a reference line onto each step in a predeterminedposition with respect to the front edge thereof, and the step ofdividing said reference lines along said line of travel so that thereference lines of each pair of two adjoining reference lines aresituated on a substantially constant mutual distance near said line oftravel, at least a number of said steps being balanced so that the frontedges thereof define an angle different from a right angle with saidline of travel.

[0002] Such a method is for example disclosed in the treatise on“Stairbuilding and handrailing” by W. and A. Mowat, published in 1989 byStobart Davies Ltd., London, and in DE-A-1 97 05 611. Both publicationsdisclose techniques for balancing the steps of a turning staircomprising fliers, i.e. steps of uniform or parallel width, and winders,i.e. steps that are narrower at one end than the other. The object ofthese balancing techniques is to make the inner end of the windersbroader so that they are more convenient and saver to walk on and sothat the pitch thereof at the inner string of the stair is less steeperwhereby a sudden and ungraceful bend, where the two different pitchedparts of winders and fliers join in with each other, is avoided. Whenbalancing the steps of a stair, the steps in the turning and one or moresteps before or after the turning are swung about the point ofintersection of a reference line, which is either their riser line ortheir front edge, with the line of travel so that this reference line isno longer perpendicular to the line of travel. The larger the number ofbalanced or dancing steps before or after the turning and the more equalthese steps are graduated on the inner string, the greater thedifference between the angle formed by the reference line of the stepswith the line of travel and a right angle, especially for the step justbefore or after the turning.

[0003] In the known balancing techniques, the line of travel is firstdivided in equal lengths, corresponding to the width of tread measuredon the line of travel. In DE-A-197 05 611, the total length of the lineof travel, including the length of the straight portions and the lengthof the circular portion is for example simply divided by the number ofsteps to achieve a constant width of tread, or distance between thereference lines, at the line of travel. Subsequently, the points ofintersection of the reference lines on the steps with the inner stringof the stair are determined. In other words, the widths of the steps aregraduated at the well, i.e. at the inner side of the stair. Thereference lines, in particular the riser lines, are then drawn betweenthe points determined on the inner string and the points determined onequal distances on the line of travel.

[0004] A drawback of the stairs designed in this way, is thatnotwithstanding the different judicious balancing techniques forgraduating the widths of the steps at the inner side of the stair, theyare not very easy to walk on, especially when more steps are balanced toa great extend before or after the turning. Another drawback is that, incase of a turning stair, just before or after the turning, a somewhatirregular nosing line is often obtained at the outer side of the stair,especially in case of a small number of relatively strongly balancedsteps just before or after a turning. This means that either anirregular wall string has to be used or that there is otherwise noconstant distance between the noses of the steps and the upper edge ofthe wall string. On the other hand, the steps could possibly be swung alittle bit manually in that irregular part to achieve a nosing lineparallel to the upper edge of the wall string. Such a correction makesthe stair however still not easy to walk on.

[0005] An object of the present invention is therefore to provide a newmethod for designing a stair which allows to obviate the above drawbacksof the existing design methods.

[0006] To this end, the method according to the invention ischaracterised in that in said dividing step, said substantially constantmutual distance is determined near said line of travel along a measuringline which is determined for each pair of adjoining reference lines soas to form a substantially constant angle with at least one of theadjoining reference lines thereof.

[0007] It has been found according to the invention that by measuringthe distances between the adjoining reference lines, i.e. in particularthe width of the treads, near the line of travel along measuring lineswhich form, in contrast to the line of travel itself, a constant anglewith at least one of the adjoining reference lines, the stair sodesigned is easier to walk on and an irregular curving of the nosingline on the outer side of the stair, just before or after a turning, canbe avoided. Compared to the prior art methods for designing a stair, thebalanced steps just before or after a turning will generally have alarger width of tread whilst the other steps will have a correspondinglysmaller width of tread.

[0008] In a particular embodiment of the method according to theinvention, the stair has two opposite ends, and, starting at least fromthe reference line on the step at a first one of said opposite ends, theadjacent reference line situated closer to a second one of said oppositeends is each time positioned on said substantially constant mutualdistance measured near said line of travel along said measuring line toform each time one of said pairs of adjoining reference lines, whichmeasuring line is determined for this latter pair of adjoining referencelines so as to form said substantially constant angle with the referenceline which is the closest to said first end and/or with the referenceline which is the closest to said second end.

[0009] In a preferred embodiment of the method according to theinvention, said substantially constant angle is an angle of between 80and 100°, preferably an angle of between 85 and 95° and most preferablyan angle of about 90°.

[0010] In a further preferred embodiment of the method according to theinvention, said measuring line has a length equal to said substantiallyconstant mutual distance and is positioned in such a manner with respectto the line of travel that a predetermined point on the measuring line,preferably the middle point thereof, is situated on said line of travel.

[0011] Other particularities and advantages of the invention will becomeapparent from the following description of some particular embodimentsof the method of the present invention. The reference numerals used inthis description relate to the annexed drawings wherein:

[0012]FIG. 1 is a schematic top plan view on a straight prior art stairwhich is entirely balanced;

[0013]FIG. 2 is a schematic top plan view on the same straight stair asshown in FIG. 1 but now designed in accordance with the method of thepresent invention;

[0014]FIG. 3 is, on a smaller scale, a schematic side elevational viewaccording to lines III-III in FIGS. 1 and 2;

[0015]FIG. 4 is, also on a smaller scale, a schematic side elevationalview according to lines IV-IV in FIG. 1;

[0016]FIG. 5 is, again on a smaller scale, a schematic side elevationalview according to lines V-V in FIG. 2;

[0017]FIG. 6 is a schematic top plan view on one step illustrating analternative measuring method;

[0018]FIG. 7 is a schematic top plan view on a quarter-turn prior artstair which is entirely balanced to achieve equal widths along the innerstrings;

[0019]FIG. 8 is a schematic top plan view on the same stair as shown inFIG. 7 but now designed in accordance with the method of the presentinvention;

[0020]FIGS. 9a, 9 b and 10 a and 10 b are schematic side elevationalviews, on a smaller scale, respectively according to lines IXa-IXa,IXb-IXb, Xa-Xa and Xb-Xb in FIG. 7;

[0021]FIGS. 11a, 11 b and 12 a and 12 b are schematic side elevationalviews, again on a smaller scale, respectively according to linesXIa-XIa, XIb-XIb, XIIa-XIIa and XIIb-XIIb in FIG. 8;

[0022]FIG. 13 is a schematic top plan view on a further quarter-turnprior art stair which is entirely balanced to achieve equal widths alongthe inner string;

[0023]FIG. 14 is a is a schematic top plan view on the same stair asshown in FIG. 13 but now designed in accordance with the method of thepresent invention;

[0024]FIG. 15 is, on a smaller scale, a schematic side elevational viewaccording to lines XV-XV in FIGS. 13 and 14;

[0025]FIGS. 16a and 16 b are, again on a smaller scale, schematic sideelevational views according to lines XVIa-XVIa and XVIb-XVIb in FIG. 13;

[0026]FIGS. 17a and 17 b are, also on a smaller scale, schematic sideelevational views according to lines XVIIa-XVIIa and XVIIb-XVIIb in FIG.14;

[0027]FIG. 18 is a schematic top plan view on a still furtherquarter-turn prior art stair, six steps of which are balanced after theturning;

[0028]FIG. 19 is, on a smaller scale, a schematic side elevational viewaccording to lines XIX-XIX in FIG. 18; and

[0029]FIGS. 20a and 20 b are, also on a smaller scale, schematic sideelevational views according to lines XXa-XXa and XXb-XXb in FIG. 18.

[0030] In the different figures, the same reference numerals designatethe same or analogous elements.

[0031] In the method according to the invention for constructing abalanced stair, this stair is first designed and subsequently materiallyconstructed. Designing of the stair can either be done manually orautomatically by means of a computer program which implements the methodsteps according to the present invention.

[0032] For designing the stair, the required dimensions are measured ofthe place where the stair has to be installed and the inner 20 and outerstrings 21 are drafted in the usual way. The outer string 21 willusually be fixed to the wall and is consequently also often called thewall string. It should be noted however that the presence of an innerand/or outer string is not an essential feature of the presentinvention, and that the stair can also be constructed without an inneror outer string. For designing the stair, the required number of steps 1to n is determined in the usual way as well as the line of travel 22.This is the line which a user normally will take when ascending ordescending the stair. It is usually drawn at a constant distance ofbetween 35 and 45 cm from the inner string 20 or, in case there is noinner string, from the inner side of the stair. In case of a newelledturning stair, the line of travel is composed of at least one straightportion followed by a circular portion having as middle point the centreof the newel 23.

[0033] According to the prevailing standards, the steps, in particularthe actual treads 24 thereof, must have a constant going or width oftread. This value is defined as the horizontal distance between thefront edges or nosings 26 of two consecutive treads 24 or, if the stepsare provided with vertical risers 25 connecting the horizontal treads 24(which is however not an essential feature of the invention since herisers can easily be omitted), the horizontal distance between the frontfaces of two consecutive risers 25. In the prior art methods, the lengthof the line of travel 22 is determined and divided by n−1 (i.e. thenumber of steps minus one) to obtain a particular mutual distancebetween the risers 25 or front edges 26, which distance is measured onthe line of travel 22 itself.

[0034] In case of an unbalanced stair, the risers 25 or front edges 26are positioned at right angles to the line of travel 22. In balancedstairs, a number of steps are swung around the fixed points ofintersection with the line of travel 22 and, in an entirely balancedstair, all the steps are swung around those fixed points. As explainedhereabove, different balancing techniques are known which can all beapplied in the method according to the present invention. Thesetechniques are based on different graduations of the width of the stepsat the inner string 20. A few balancing methods are described on pages67 to 72 of the treatise on “Stairbuilding and handrailing” by W. and A.Mowat, which is incorporated herein by way of reference. Also the otherparts of this treatise, which disclose how to design different types ofstairs, is included herein by way of reference. Since the differentbalancing techniques are well known by a person skilled in the art, theywill not be described herein in detail. Amongst the known balancingtechniques, mention can be made of the trap method (with a lineardecrease of the width of tread at the inner string towards the newel orthe centre of the turning), the harmonic balancing, the balancing in theinfinity and, for straight stairs, the warped stair which is a straightstair, the steps of which are swung in such a manner that their frontedges are not perpendicular to the line of travel. These techniques aredescribed in “Trappen” by H. Van Daele and V. Seys edited by De Sikkel,which is also incorporated herein by way of reference. A furtherbalancing technique consists in dividing the inner string into equalportions. In this way, a straight inner string, and consequently astraight hand railing is obtained, which results in an economical stairand which is therefore preferred according to the invention. Once theline of travel 22 has been divided into equal parts and the points ofintersection of the risers 25 or the front edges 26 of the steps withthe inner string 20 have been fixed with one of the balancingtechniques, the risers 25 or front edges 26 can simply be positioned ordrawn.

[0035] The method according to the present invention differs from theabove described prior art methods in that the line of travel 22 is notdivided in equal parts measured on this line 22 itself. Instead, themutual distance between the successive risers 25 or front edges 26 isdetermined along a measuring line 27 which is determined for each pairof adjoining risers 25 or front edges 26 so as to form a substantiallyconstant angle with at least one of the adjoining risers 25 or frontedges 26. Since for a balanced stair, the line of travel 22 does notform a constant angle with the risers 25 or front edges 26 of each ofthe steps, the steps designed by the method according to the presentinvention have another shape and orientation than the steps designed bythe prior art methods.

[0036] Instead of taking the riser 25 or front edge 26 of a step asreference line for designing the stair, another reference line can bedetermined onto each step in a predetermined position with respect tothe front edge 26 thereof. Once the reference lines have been positionedon said substantially constant mutual distances in accordance with themethod according to the invention, the risers 25 and front edges 26 canbe drawn in said predetermined position with respect to the referencelines. These reference lines are preferably parallel to the front edge26 and coincides most preferably with this front edge 26. Consequently,in the further description the front edges 26 of the steps will be takenas reference lines. This offers the advantage that when dividing thefront edges 26 on constant mutual distances at the inner string 20, anentirely straight inner string 20 and handrailing can be used, which isvery economical. Such an entirely straight string 20 would for examplenot be obtained when dividing the risers 25 on equal distances at theinner string 20 in view of the fact that at least a number of the stepsare balanced so that there is not a constant distance between the frontedges 26 and risers 25 of the steps measured in the longitudinaldirection of the inner string 20. Of course, when the steps are balancedon the inner string 20 in such a manner that a curved string 20 isobtained, this is of no or less importance.

[0037]FIG. 1 shows a top plan view on a straight stair designedaccording to the prior art method. This stair comprises a straight innerstring 20, a straight outer or wall string 21, steps numbered from 1 to15 represented by their front edges 26 and in dashed lines by theirrisers 25, and a lower and an upper newel or post 23. At the innerstring 20, the front edges 26 are positioned at constant mutualdistances so that a straight inner string 20 is obtained as shown inFIG. 3. At the line of travel 22, the constant mutual distances dbetween the front edges 26 are measured on the line of travel itself sothat in this case also a substantially straight outer string 21 isobtained as shown in FIG. 4. A drawback of this stair designed accordingto the prior art method is that it is not very easy to walk on.Especially when descending this stair, one will not feel very well atease when arriving nearly at the bottom of the stair since one will havethe impression that the steps are relatively narrow at that endnotwithstanding the fact that they have a same width of tread measuredon the line of travel 22.

[0038]FIG. 2 shows the same straight stair as illustrated in FIG. 1 butnow designed by the method according to the present invention. At theinner string 20, the front edges 26 are again on a same constant mutualdistance so that the same inner string 20 as illustrated in FIG. 3 isobtained. However, at the line of travel 22, the constant mutualdistances d between the front edges 26 are no longer measured on theline of travel 22 but on measuring lines 27 which form a substantiallyconstant angle α of 90° with one of the front edges 26 of each pair ofadjoining front edges, in the embodiment of FIG. 2 each time with thelowermost front edge 26. Although this angle α may be chosen within widelimits, preference is given to an angle α of between 80 and 100°, moreparticularly to an angle α of between 85 and 95° and most preferably toan angle α of about 90°. An angle α close to or equal to 90° isespecially preferred in case of a turning stair which is not balanced toa great extend so that quite wedge shaped winders are present in theturning. The angle α is on the other hand less important in case ofstrongly balanced stairs wherein the angle defined by two successivefront edges is rather constant or wherein there are no pronouncedwinders.

[0039] For designing the stair illustrated in FIG. 2, the front edges 26of the uppermost step 15 and of the lowermost step 1 are first drawn inthe desired position. Subsequently, the points of intersection of thefront edges 26 with the inner string 20 are fixed on mutually constantdistances. Then, starting from the front edge 26 of step 15 at theuppermost end of the stair, the front edge 26 of step 14 is positionedon said constant distance d measured along the measuring line 27 whichforms a right angle α with the front edge 26 of step 14. The measuringline 27 has more particularly a length equal to distance d and ispositioned in such a manner that the middle 28 of this measuring line 27is situated on the line of travel 22. Instead of the middle point 28,another point situated on the measuring line 27 could be taken as pointof intersection with the line of travel 22, for example one of the endpoints or a point therebetween.

[0040] Once the front edge 26 of step 14 is positioned in this way, thefront edge 26 of step 13 and subsequently of the further steps situatedcloser to the lowermost end of the stair are positioned in the same way.

[0041] Compared to the distance d in FIG. 1, the distance d in FIG. 2 issomewhat smaller in order to achieve the same total stair length. Thedistance d can therefore not be determined by simply dividing the totallength of the line of travel 22 by the number of steps n minus one. Inpractice, a somewhat smaller distance d can be taken to start with. Ifit appears that by means of the selected smaller distance d, the frontedge 26 of the lowermost step 1 extends beyond the lower end of thestair, i.e. extends beyond the predetermined position for this lowermostfront edge, the distance d is reduced somewhat further and the frontedges 26 of the different steps are positioned again. If the front edgeof the lowermost step still extends beyond its predetermined position,distance d is further reduced. On the other hand, if it does not extendfar enough, an intermediate distance d is selected until the front edge26 of the lowermost step coincides sufficiently accurately with itspredetermined position.

[0042] The above described method can be performed manually by theperson skilled in the art, who, once acquired some experience, will onlyhave to repeat the above process a few times. On the other hand, themethod can also be performed by a computer programmed to calculate thedifferent positions of the front edges 26 and to modify distance d untilthe front edge 26 of the lowermost step is in the predeterminedposition.

[0043] In a first variant embodiment for positioning the front edges 26on substantially constant mutual distances d, the angle α between thefront edges 26 and the measuring lines 27 can also be adapted in such amanner that the front edge 26 of the lowermost step 1 is positioned inthe desired predetermined position. Indeed, the smaller angle α, thesmaller the total length of the stair and vice versa, the more angle αapproaches 90°, the larger the total length of the stair whenpositioning the successive front edges in accordance with the methoddescribed hereabove.

[0044] In this respect, it should be noted that the angle α should notnecessarily be an angle of 90°. In the stair of FIG. 2, it makes nodifference when this angle α comprises for example about 80° (=α′) oreven smaller. Of course, in that case, the distance d′ measured in thismore oblique way, will be greater than the distance d, but the frontedges 26 of the steps will be positioned in substantially the sameposition (see the measuring lines 27 indicated in broken lines in FIG.2).

[0045] In a further variant embodiment, the measuring lines can also bedrawn or positioned at the constant angle α with respect to the frontedge 26 of the uppermost step of each pair of steps, i.e. starting fromthe front edge 26 of step 15. Again, this angle α does not necessarilyhave to be an angle of 90°.

[0046] In still another variant embodiment, the measuring line can bedetermined for each pair of adjoining front edges to form saidsubstantially constant angle α with for example the uppermost edge 26and a further substantially constant angle β with for example thelowermost front edge 26. Just like the angle α, the angle β ispreferably comprised between 80 and 100°, more preferably between 85 and95° and may comprises in particular 90°. In this variant embodiment, usecan for example be made of a curved measuring line, having asubstantially constant length but the curvature radius of which isadapted to form said substantially constant angles α and β with theadjoining front edges 26. On the other hand, use can be made of a brokenmeasuring line showing a kink. The angle under which the measuring lineis broken can be adapted for each pair of adjoining front edges toachieve the desired angles α and β.

[0047] A practical embodiment wherein angles α and β equal about 90° isthe embodiment illustrated in FIG. 6. In this embodiment, use is made ofa circles 29 having a centre 30 and a substantially constant diameter.This circle 29 is positioned with its centre 30 onto the line of travel22 in such a manner that the front edge 26 which has already beenpositioned is tangent to this circle. The next front edge 26 is thenpositioned so as to be tangent to the circle 29. In this way, themeasuring line 27, which has a length equal to the diameter of thecircle 29 and which is composed of the two radii going though the twopoints of contact 30, forms an angle α and β of 90° with the front edges26. Notwithstanding the fact that in this embodiment with the circlesthe measuring lines are not actually drawn, the substantially constantmutual distance d is still inherently determined along the measuringlines 27.

[0048]FIG. 7 shows a quarter turn stair designed in accordance with theprior art method and FIG. 8 a same quarter turn stair designed inaccordance with the method according to the invention. The inner string20 of this quarter turn stair consists of a lower part 20′ and an upperpart 20″ whilst the outer string 21 also consists of a lower part 21′and an upper part 21″. Instead of starting from one end of the stair,the front edges 26 of the lowermost 1 and uppermost step 15 of the stairillustrated in FIG. 8 were now positioned starting from both ends of thestair. Both starting from the upper and the lower end of the stair, thesame mutual distance d and the same angle α (equal to 90°) was used.

[0049] The front edge 26 of the step 6 right in the middle of theturning was positioned each time starting from both ends. The mutualdistance d was modified until this front edge 26 was positioned insubstantially the same position both when starting from the upper andfrom the lower end of the stair. In this way, the method according tothe invention is applied in the same way to the parts of the stairbefore and after the turning, i.e. each time in the direction from therespective end of the stair towards the turn. It will be clear that thesame variants or modifications can be applied to this embodiment asdescribed hereinabove for the embodiment of FIG. 2.

[0050] When comparing the stairs of FIGS. 7 and 8, it can be seen thatin the stair designed according to the prior art method, the step 4 justbefore the turn and especially the step 8 just after the turn arenarrower than the first or the last steps whilst this is not the case inthe stair according to the invention illustrated in FIG. 8. As a firstresult thereof, the stair of FIG. 7 is less easy to walk on than thestair of FIG. 8, especially when descending the stair. A further resultis that the stair of FIG. 8 has a more regular nosing line 31 at theouter string 21.

[0051] The inner sides of the inner strings 20′ and 20″ of the prior artstair are illustrated in FIGS. 9a and 9 b. Since the front edges 26 ofthe steps are divided over the inner string at regular distances, bothinner string parts 20′ and 20″, and thus also the hand railing which hasnot been illustrated, are entirely straight. This is also the case forthe inner strings 20′ and 20″ of the stair according to the inventionillustrated in FIGS. 11a and 11 b respectively.

[0052] The outer strings 21′ and 21″ are however curved due to thebalancing of the steps, more particular over their entire length sincethe stair is a completely balanced stair. As can be seen in FIGS. 10aand 10 b, the method according to the prior art results in an irregularnosing line 31 (comprising a straight portion for steps 1-5, a kinkafter step 5 and before step 8, and again a straight portion for steps8-15). Indeed, especially for steps 7 and 8, it can be seen that thereis a greater distance between the front edges 26 and the top of theouter string 21 which has been drawn, in contrast to the nosing line 31,according to a flowing line. In practice, this is of course not a nicelyfinished stair. Consequently, one could try to remedy this defect bymaking steps 7 and 8 for example wider, but this would make steps 2 and6 too narrow. The stair would therefore still be not easy to walk on.

[0053] As can be seen in FIGS. 12a and 12 b, the method according to theinvention results in a smooth nosing line 31. The top of the outerstring 21 can therefore be drawn at a constant distance from the nosings26 so that a nicely finished stair is automatically obtained. This stairis moreover easier to walk on since all the steps have the same width.An essential difference with the prior art stair is that the steps atthe lower and upper ends of the stair have a somewhat smaller width oftread so that at these ends, the outer strings 21′ and 21″ are somewhatsteeper.

[0054]FIG. 13 shows a completely balanced prior art quarter turn stairhaving its turn at its lowermost end. FIG. 14 shows a same stair,designed in accordance with the method according to the invention(starting from the front edge of the uppermost step 15 and measuringdistance d according to a measuring line 27 which is perpendicular(angle α=90°) to this front edge and which intersects the line of travel22 with its middle point 28, for aesthetic reasons, the lowermost stephas however been made somewhat broader or deeper). Again it can be seenthat step 5 of the prior art stair is considerably narrower than thesteps at both ends, in particular about 3 cm when the uppermost step hasa width of about 19 cm.

[0055] The inner string is for both stairs the same straight stringwhich has been illustrated in FIG. 15. The outer strings 21′ and 21″ ofthe prior art stair are shown in FIGS. 16a and 16 b. It can be seen thatfor step 5, just after the turn, there is a considerably greaterdistance between its nosing 26 and the smooth top of the outer string21″ whilst for step 3 the nosing 26 extends nearly to the top of outerstring 21′. This is of course not aesthetic. The irregular distance fromthe nosing line 31 to the top of the outer string 21 is due to the factthat the nosing line 31 is not a flowing line. In fact, from step 15 tostep 6, the nosing line is nearly a straight line. This means that thetransition from the concave top of the uppermost outer string 21″ to theconvex top of the lowermost outer string 21′ has to be achieved over avery short distance. This results of course in abrupt bendings or inother words in a non-smooth line.

[0056] In the stair designed according to the method according to theinvention, the nosing line at the outer strings 21′ and 21″ is a smoothline which starts already to curve from the uppermost steps 15, 14, 13,. . . In this way, there is obtained a smooth transition between theconcave and convex tops of the strings 21″ and 21′, without any abruptcurving at the step 5 just after the turn.

[0057]FIG. 18 illustrates a prior art stair which differs from the stairillustrated in FIG. 13 in that the uppermost steps 10-15 are notbalanced. Only steps 1-9 are balanced, more particularly according tothe harmonic balancing method. Due to this harmonic balancing technique,the inner string, which is illustrated in FIG. 19, is curved, startingfrom step 9, according to a smooth line. However, notwithstanding thisbalancing technique, it appears that especially step 5 is not deepenough to walk easy on the stair. Moreover, the nosing line 31 at theouter string 21″ consists from the top to the bottom successively of twostraight portions, namely for steps 15 to 10 and for steps 9 to 6, afterwhich there is a sudden curve over the nosings of steps 5 and 4. Whenthe top of the outer string 20″ has been made more smoothly asillustrated in FIG. 20b, this results in a too large distance betweenthe nosing of step 5 and the top of the outer string 21″. Just as forthe stairs illustrated in FIGS. 13 and 14, this drawback can be obviatedby applying the method according to the present invention but this hasnot been illustrated in the drawing.

[0058] From the above description of some particular embodiments of themethod according to the invention, it will be clear that manymodifications can be applied thereto without leaving the scope of theinvention as defined by the appended claims.

[0059] It will especially be clear that the method for measuring themutual distances d can be applied in combination with any existingbalancing technique and to many different kinds of stair. It can forexample not only be applied to balanced straight stairs or quarter-turnstairs but also to half-turn stairs. The stairs may further be so-calledgeometrical stairs which do not have a newel in their turns. In order toavoid sudden bends in the-inner strings or in the handrailing of suchstairs in the turning, the steps before and/or after the turn should bestrongly balanced. Especially in this case, the method according to theinvention provides a large improvement over the known methods.

[0060] Of course, the stairs may be made of different materials andassembled in any known way without leaving the scope of the invention.

1. A method for constructing a balanced stair comprising steps withtreads showing front edges, which method comprises the step of designingthe stair and the step of materially constructing the stair so designed,the designing step comprising the step of determining a line of travelon the stair, the step of determining a reference line onto each step ina predetermined position with respect to the front edge thereof, and thestep of dividing said reference lines along said line of travel so thatthe reference lines of each pair of two adjoining reference lines aresituated on a substantially constant mutual distance near said line oftravel, at least a number of said steps being balanced so that the frontedges thereof define an angle different from a right angle with saidline of travel, characterised in that in said dividing step, saidsubstantially constant mutual distance is determined near said line oftravel along a measuring line which is determined for each pair ofadjoining reference lines so as to form a substantially constant anglewith at least one of the adjoining reference lines thereof.
 2. A methodaccording to claim 1, characterised in that said reference lines aredetermined on said steps either parallel to or coinciding with the frontedge of said steps.
 3. A method according to claim 1 or 2, characterisedin that said substantially constant angle is an angle of between 80 and100°, preferably an angle of between 85 and 95° and most preferably anangle of about 90°.
 4. A method according to any one of the claims 1 to3, characterised in that the stair has two opposite ends, and in that,starting at least from the reference line on the step at a first one ofsaid opposite ends, the adjacent reference line situated closer to asecond one of said opposite ends is each time positioned on saidsubstantially constant mutual distance measured near said line of travelalong said measuring line to form each time one of said pairs ofadjoining reference lines, which measuring line is determined for thislatter pair of adjoining reference lines so as to form saidsubstantially constant angle with the reference line which is theclosest to said first end and/or with the reference line which is theclosest to said second end.
 5. A method according to claim 4,characterised in that said measuring line is determined so as to formsaid substantially constant angle with the reference line which is theclosest to said first end and so as to form a further substantiallyconstant angle with the reference line which is the closest to saidsecond end.
 6. A method according to claim 5, characterised in that saidfurther substantially, constant angle is an angle of between 80 and100°, preferably an angle of between 85 and 95° and most preferably anangle of about 90°.
 7. A method according to claim 6, characterised inthat use is made each time of a circle, having a centre and a diameterequal to said substantially constant mutual distance, for positioningsaid adjacent reference line situated closer to said second oppositeend, which circle is positioned with its centre substantially onto saidline of travel so that the reference line situated near said first endis tangent to this circle and the adjoining reference line situatedcloser to said second end is positioned so as to be also tangent to thecircle.
 8. A method according to any one of the claims 4 to 7,characterised in that starting from the reference line on the step atsaid first opposite end, the adjacent reference line situated closer tosaid second opposite end is each time positioned on said substantiallyconstant mutual distance until the reference line of the step at saidsecond end of the stair is positioned and when this latter referenceline is positioned in such a manner that the front edge of this stepdoes not substantially coincide with the second end of the stair,positioning of the reference lines is started again either with asmaller substantially constant mutual distance and/or with asubstantially constant angle which differs more from a right angle incase the front edge of the step at said second end extends beyond thisend or with a greater substantially constant mutual distance and/or witha substantially constant angle which differs less from a right angle incase the front edge of the step at said second end does not extend up tothis second end.
 9. A method according to any one of the claims 4 to 7,characterised in that starting from the reference line on the step atsaid first opposite end, the adjacent reference line situated closer tosaid second opposite end is each time positioned on said substantiallyconstant mutual distance and starting from the reference line on thestep at said second opposite end, the adjacent reference line situatedcloser to said first opposite end is each time positioned on saidsubstantially constant mutual distance until a predetermined referenceline is positioned both starting from said first end and from saidsecond end and when this predetermined reference line is positioned notin substantially the same position when starting from the first and thesecond end of the stair, positioning of the reference lines is startedagain either with a smaller substantially constant mutual distanceand/or with a substantially constant angle which differs more from aright angle in case the predetermined reference line positioned startingfrom the first end of the stair extends beyond the predeterminedreference line positioned starting from the second end of the stair orwith a greater substantially constant mutual distance and/or with asubstantially constant angle which differs less from a right angle incase the predetermined reference line positioned starting from the firstend of the stair does not extend up to the predetermined reference linepositioned starting from the second end of the stair.
 10. A methodaccording to any one of the claims 1 to 9, characterised in that saidmeasuring line has a length equal to said substantially constant mutualdistance and is positioned in such a manner with respect to the line oftravel that a predetermined point on the measuring line is situated onsaid line of travel.
 11. A method according to claim 10, characterisedin that said predetermined point is situated substantially in the middleof said measuring line.